Research On The Robust Control And Filtering For Distributed Delay Systems

The research on networked control systems by the domestic and overseas scholars is increasing,and a series of achievements have laid a theoretical foundation for the development of network control system.The introduction of communication Internet will cause the phenomena of time delays and packet losses,which can be treated as equivalent delays in continuous systems.Among various of time-delay systems,system with distributed delays will arise in such circumstances when the number of summands in a system equation is increased and the differences between neighboring argument values are decreased.For instance,One application of distributed delay systems can be found in the modeling of feeding systems and combustion chambers in a liquid monopropellant rocket motor with pressure feeding.From an objective point of view,distributed delays can describe the system more profoundly and accurately,revealing the nature of things change.Consequently,it is of great practical significance to study the networked control systems with distributed delays.In addition,it is also necessary to consider the influence of the uncertainty on the system caused by the mathematical modeling error,the condition changes and the external disturbance.In this paper,the problems of robust control and robust filtering for distributed delay systems are studied,and the simulation results show that the methods proposed in this paper is feasible and effective.First of all,different problems of designing controller for the distributed delay systems are studied.On the one hand,considering the distributed delay systems with actuator failures,this paper is concerned with the design problem of fault-tolerant H? controller.First,the time delays and packet dropouts in communication network are treated as equivalent delays,and combined with the actuator fault matrix,the closed-loop control system is established.Second,based on Lyapunov stability theory,a fault-tolerant H? criterion guaranteeing the asymptotic ability of the closed-loop NCSs is formulated.Furthermore,by utilizing the linear matrix inequality(LMI)technique,the method for obtaining controller parameters is given.Finally,the effectiveness of the proposed method is validated by the simulation.On the other hand,the problem of designing L2-L? controller for the distributed delay systems is also studied.Secondly,this paper concentrates on investigating the robust control and filtering problem for the uncertain distributed delay systems on the basis of choosing different performance indexes.Considering the distributed delay systems with uncertainties,different controller and filter are designed based on the difference of requirements,then the corresponding closed-loop system is established by utilizing the augmented state method.Furthermore,a sufficient condition guaranteeing the prescribed performance is derived,andthe linear matrix inequalities are given to obtain the coefficients of controller and filter.Finally,the effectiveness of the proposed method is verified by the numerical examples.Lastly,the L2-L? filtering for the nonlinear distributed delay systems described by T-S fuzzy model is studied.The parallel distributed compensation(PDC)is used to defuzzify the controlled object and fuzzy filter,then the filtering error system with distributed delays is established.By constructing a proper Lyapunov function,the L2-L? performance criterion guaranteeing the asymptotic stability of the filtering error system is formulated.According to the linear matrix inequality technique,the congruence transformations and variable substitutions,the method for obtaining the filter parameters is given as a series of matrix inequalities,and furthermore,the problem of obtaining the filter parameters is converted into a convex optimisation problem.Finally,a numerical example is presented to demonstrate the feasibility and effectiveness of the proposed method.